find the first 3 terms in Maclaurin series for sin^2x. find taylor series for e^-x at a =-4 in general form

Question

1) sin^2x

2) xe^-x

3) Find Taylor series for e^-x    at a= -4 in general form

 

Answer 1

Formulas and derivation for the terms and general form of Taylor and Maclaurin series can be readily found from your text and on the WEB. using these we obtain,

 

Maclaurin sin(2*x) = 2x - 4x³/3 + 4x⁵/15 + ...

 

Maclaurin xe^-x = x - x² + x³/2 + ...

 

Taylor General Form e^-x  about x=-4 = ∑(-1)ⁿe⁴(4+x)ⁿ/n! summed from n>=0 to inf.